Question: Rewrite as a simplified fraction. ${0.7\overline{6} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 76.6666...\\ 10x &= 7.6666...\end{align*}}$ Subtracting the two equations, we have: ${90x = 69}$ ${x = \dfrac{69}{90}} $ ${x = \dfrac{23}{30}} $